What is expand ln((10^{-4}x^{-2})/(x^5)) ?

The solution to expand ln((10^{-4}x^{-2})/(x^5)) is -4ln(10)-7ln(x)

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expand ln((10^{-4}x^{-2})/(x^5))

expand

ln (\frac{1 0 ^{- 4} x ^{- 2}}{x ^{5}})

- 4 ln (10) - 7 ln (x)

Solution steps

ln (\frac{1 0 ^{- 4} x ^{- 2}}{x ^{5}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{1 0 ^{- 4} x ^{- 2}}{x ^{5}}) = ln (1 0^{- 4} x^{- 2}) - ln (x^{5})

= ln (1 0^{- 4} x^{- 2}) - ln (x^{5})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{5}) = 5 ln (x)

= ln (1 0^{- 4} x^{- 2}) - 5 ln (x)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (1 0^{- 4} x^{- 2}) = ln (1 0^{- 4}) + ln (x^{- 2})

= ln (1 0^{- 4}) + ln (x^{- 2}) - 5 ln (x)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (1 0^{- 4}) = - 4 ln (10)

= - 4 ln (10) + ln (x^{- 2}) - 5 ln (x)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{- 2}) = - 2 ln (x)

= - 4 ln (10) - 2 ln (x) - 5 ln (x)

Add similar elements:

- 2 ln (x) - 5 ln (x) = - 7 ln (x)

= - 4 ln (10) - 7 ln (x)

ln (k) + 2 ln (7 r)

2 ln (x + 2) - ln (x + 2) - ln (2) - 3

ln (\frac{x ^{p} e ^{- y}}{z})

ln (x^{5} y^{3})

lo g_{10} (5 + x) - 2 lo g_{10} (x + 4)

What is expand ln((10^{-4}x^{-2})/(x^5)) ?
The solution to expand ln((10^{-4}x^{-2})/(x^5)) is -4ln(10)-7ln(x)